Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba-bility mass functionP(Xi = x₁) =0(1-0)¹-il, a; € (-1,0,1), 0≤0≤1.a. Derive the MLE Ô for 0.b. Assuming n is large, find the approximate distribution of .c. Find an approximate 95% confidence interval for 0.d. Derive the likelihood ratio test for testing 0 = 1/2 vs. 0 > 1/2.

a. To find the maximum likelihood estimator (MLE) of theta, we need to maximize the likelihood…

Answered: Problem 4. Let X = (X₁, X2,..., Xn) be…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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(4) A closed rectangular container with a square base is to have a volume of 2250in². The material for the top and bottom of the container will cost $2 per in², and the material for the sides will cost $3 per in2. Find the dimensions of the container of lest cost. (5) Let s(t) = t³ - 9t2 +24t be the position function of a particle moving along a coordinate line where s is in meters and t is in minutes. (a) Find the velocity and acceleration functions, (b) Find the position, velocity, speed, and acceleration at time t = 1 (c) At what time is the particle stopped? (d) When is the particle speeding up? Slowing down? (e) Give a schematic picture of the motion, (f) Find the maximum speed of the particle during the time interval 0 < t < 5, (g) Find the total distance traveled by the particle from time t = 0 to t=5. (6) Verify that each function satisfies the hypothesis of the Mean Value Theorem on the interval [a, b]. Then find all the numbers c that satisfy the conclusion of the Mean Value…
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Problem 4. Let X = (X₁, X2,..., Xn) be i.i.d. where each X, has proba- bility mass function P(X = ) - (9) (1-0)¹-1, ₁ € (-1,0,1}, 0≤ 0≤1.